Retailers have warned of a "massive disruption" to food supplies ahead of the easing of all remaining restrictions on Monday.
A senior M&S executive told the Sunday Times that there may not be enough staff to open stores because of increasing infections and the number of people self-isolating.
"Our Covid cases are roughly doubling every week and the pinging level is about three to one of Covid cases, so we’re seeing that growing exponentially," he said.
Steve Rowe, chief executive of M&S, added: “If there’s shortages we’ll have to manage it by changing hours of stores, reducing hours.
"Where the industry will see the pain is in the supply chain because logistics runs tight anyway to be efficient.”
Any disruption in the supply chain could mean empty shelves as supermarkets struggle to keep up with demand.
Tim Morris, chief executive of the UK Major Ports Group, called the “pingdemic” the most “significant threat to ports’ resilience we have seen yet”.
He said: “If the current trajectory of absences continues without the Government taking any action, there has to be a risk of disruption to important supply chains, including food.”
The NHS app sent a record 520,194 alerts last week, instructing users to quarantine for up to ten days because they had been in close contact with someone who had tested positive for coronavirus.
According to the Telegraph, meat processors also reported that one in 10 of their workforce were being told to self-isolate by the app, in a development that could require firms “to start shutting down production lines altogether”.